Hi there,
My partner is an INTP who is similar to you in that he is a raging rational atheist. (OK - perhaps you're not raging, I certainly don't want to assume, but you might be, at least from the perspective of those with a compatibly raging religious inclination). Oh and we're also a biracial couple - woot! Living in sin - woot! woot!! And very liberal, progressive, humanitarian in our world views - woot! woot!! WOOT!!!. One site said we're both misfits who "get each othe, in often outspoken ways". Ding. So true. We share lively banter and often talk about many ideas and issues that are important or interesting to us. We also both possess analytical minds - and are both deep thinkers. People find us probably abrasive and arrogant (especially moi, since I'm a petite 'lil Azian huny - yo!" People give me a once over and assume I'm a sweet-natured, docile pussy cat, but no I really have the heart and mind of a conquistador, lol (I stole that from the 5 foot tall asian entj poster - very funny, I totally hear you sista ;-) ) Overall I think we're great together - but then again, we both are, we like to think, emotionally mature (I think that kicks in once you've got some life experience under your belt, worked on parts of yourself and am not afraid to be who you are, but also be aware of other's social,/emotional needs e.g. we're both in our mid 30's, life has knocked us around a bit and we're still standing, yeah, yeah yeahh!!! I do go out more often than my happy-to-stay-at-home-and-read-or-work-out-a-very-abastract-problem-on-the-computer INTP. We both are very independent in our natures; so we allow for a generous amount of apart time as well as together time (hiking, camping, travelling, film viewing, attending lectures, talking, eating, sex, playing with our pussy . . . . cat).

So in my experience, an INTP works for me. I also think an INFJ or INFP would work also.
Cheers!