It is possible, but there is more info needed
How high are taxes and insurance in that area you are looking?
Is the car loan the only debt you have or are there any school loans/credit cards?
How recently were the charge offs, and has there been good credit reestablished?
Last, generally, unless the two of you are going into this together as a long term investment/rental property that the two of you are planning on living in initially, I would advise against 2 young adults (this may not be the case, but that is the impression I get from the post, job histories, income levels, school info) going in and buying a house together. The reason is that you guys (assuming I am correct on the younger adults part) are both in what is generally a transformative time of life, The odds that one of the two of you may meet someone/move/get married/move for work in the next 5 years are pretty high. It does not appear currently that either of you could afford the home on your own. If one had to move, that persons credit (DTI especially) would be tied up in the home because it may be awhile before either of you would be able to refi the mortgage on your own. Again, if both parites are going into this thinking that you both want to keep the house for an investment if something were to happen a few years down the road, it is another story. If that were the case though, it needs to be set up very specifically so any future situation are addressed.
As far as interest rate goes, FHA rates are near historical lows (although up slightly and definitely on the way up right now) so I would not worry about the rate.
