Once a cheater always a cheater. Listen to PP who tried and stuck it out too long. I'm sorry, OP.

OP here. DH had an affair, says it's over, says he wants to repair things. I asked for him to leave (he is living at his parents) because I thought we needed some space to figure things out. Right now, we are both saying we want to work towards him moving back in. There's the affair to work through but also a bunch of other stuff including mental health, substance abuse, and professional. We're going to therapy individually and together. I think we are both honest in our intentions. At the same time, some of the things to work through aren't instant fixes and I think realistically this is a 3-6 month separation. I guess I just want to make sure I don't make stupid mistakes in navigating this. We are not seeing other people (I know that's a leap of faith for me to believe him), yet how much time and what kind of time (and physical relationship) we have together seems like a moving, fraught target.

PP here. This is an example. Many marriage counselors recommend it but only for 3-6 months.
Sample CS® Contract
1. Time Limits: I agree to a ____month separation commencing on (date)__________ .
2. Legal Counsel: I will/will not contact an attorney in order to become informed. I agree not to make any efforts to file for divorce/will put divorce on hold for 3-6 months during the life of this contract.
3. Living arrangements: ________________ will move out on (date)_____________ .
4. Dividing Home Furnishings: I agree to cooperatively divide household goods to ensure maximum comfort in our separate living quarters.
5. Finances: I agree to make as few changes in our finances as possible.
6. Children: a.)I agree to flexible and cooperative child-care arrangements. I agree to give 24 hours advance notice for special events.
b.) I agree to develop a timeline and a script for telling the children about the separation.
7. Pet Care: I agree to be flexible and cooperative with care and attention for our pet(s).
8. Couple’s Interpersonal Relationship:
a. Telephone: I will phone my spouse ____ times weekly for the purpose of __________________ I will telephone the children ______times weekly.
b. (optional)E-mail: I will e-mail my spouse ____ times weekly for the purpose of __________________ . I will e-mail the children ______times weekly.
c. Entering Spouse’s Residence: _____________________________________
d. Household Repairs: _____________________________________________
e. Family Outings: ________________________________________________
f. Holidays: ______________________________________________________
g. Frequency of Dating and Permissions of Sexual Contact with spouse: (who asks who out first?)
__________________________________________________________________
9. Dating Others: I do/do not intend to date others.
10. Confidentiality: Concerning parents and friends – I agree to limit explanations of the details of this contract to discourage unnecessary gossip. I respect that there are both public and private considerations and agree to what those are. I also agree to refrain from maligning
my spouse and will not encourage others to take sides.
11. Professional Resources: I agree to coaching/counseling, and/or mediation if either party is unable to negotiate any of the given terms of this contract in an amicable manner.
12. Homework: I agree to do all homework as assigned with the facilitator.
13. Contract: No changes will be made in this contract unless both partners agree to the terms.
14. Termination of Contract: I agree to inform my spouse verbally or in writing of my intention to terminate this contract.
Signed: ______________________________________
Date:________________
Signed: ______________________________________
Date:________________

"Separation" means one person wants to go fuck somebody else and have the option to come back if that doesn't work out.

Recipient of "separation" request should say forget it, either get divorced or commit to this marriage.

I did it. We did a controlled separation which is basically a contracted agreement answering questions such as will you date each other or others, money arrangements, how often will you see each other. If you google controlled separation you can find sample contracts.

I fell back in love. We reconciled and moved back in together. For two months things were great. Then the old patterns started. We stuck it out for almost three more years. That's how long it took me to accept that I can't be married to him.

Take your time if you need it OP. I had to know I tried everything. Maybe it will work for you, all dependant on the issues I guess.

You don't know until you know, but if it's worth anything I would suggest just working towards divorcing now.

There's a book by Mira Kirshenbaum called "too good to leave, too bad to stay" it's a step by step guide that you might find helpful. It gives accounts of people who stayed or left and how they felt tied directly to all sorts of individual issues.
https://www.amazon.com/Good-Leave-Stay-Step-Step-ebook/dp/B002JPGQ34

Woman initiating separation ? If so, skip it and get divorced. You've already made your decision you just have the balls to admit it.
In general bad idea

Has anyone been separated, gotten back together, and had the marriage be the better for it? What's your advice about navigating that route? Things you wish you did/didn't do? Things that in hindsight really made the difference?