On an H-1B visa, most lenders will decide the status of a mortgage applicant on a case-by-case basis by utilizing the information available to them. The following is required by most lenders...

SSN

Valid work visa

2 years US credit history

2 years US employment history

Good credit score, ideally over 670

US income that you expect to continue for at least 3 years

If you are applying for an FHA loan, you will need an Employment Authorization Document (EAD) from the USCIS.