I work at a nursery. Dill does fine here, but it goes to seed in our climate pretty fast and so you'll need to replant as a PP says. Also, it won't taste like it would in a cooler climate -- but it will grow.
Flat and curly leaf parsley grow very well here, they taste fine, and you won't need to replant. DO cut these back, hard.
I respectfully disagree with 10:50 - cilantro hates the DC humidity and heat. It gets leggy, yellow, and loses its flavor immediately, within a couple weeks. We tell customers to expect that they'll be replanting it every two weeks. (and then, what's the point, really?)
If I HAD to have it planted, I guess I'd try it on the windowsill.
Cilantro does fine here. It is not a heat and humidity thing. Leggy, yellow is a lack of sun. I plant two three rows every year. It and basil are the best performers in spice terms for this area. It is alway in the farmers market. Maybe you are growing it is pots or something.