My answer may be little too late unless if you are still in the market for the house and your immigration status is still H1B. If it has changed to approved I 140 with I 797 and an EAD card has been issued to you. You do not have any problem in buying a house and getting the loan.
However, H1B with EAD is recognized by all the banks and Fannie / Freddie as well. While FHA recognozes only EAD though little persuation can get you FHA loan as well on H1B.
There is no problem in getting it approve. I specialize in those loans and you can call me or get on my web site for the details. http://www.atulrastogi.com (908) 798 3560
As a former immigration attorney, I would suggest you continue to remain prudent in your approach. New Jersey is an at-will employment state, so continued employment is not guaranteed.
Presently, as you know, your non-immigrant status implies that you will return to your home country. You do not indicate where you are in the immigrant process, e.g., whether the labor certification or the I-140 is pending.
Please give me a call
I would certainly be willing to discuss the specifics of your case to help you make an educated decision about how to best proceed.
There is no problem to obtain a loan as a non-immigrant. Any green card holder can get a loan and in fact with your H1B visa you can also get a loan. Of course it would be prudent to gate your green card prior to buying a home. Dan Sukhia