Myself and girlfriend both own property, but would like to sell and buy together... one has neg equity?

We'd really like to sell both and buy our 1st home together. However, one has negative equity (approx 10k) due to recent recession and the other has approx 25k equity. We were both made redundant last year and consequently had some arrears on our mortgages but they were quite low and we've almost caught back up now. So... how would we stand if we were to sell one house but keep the one with neg equity and maybe rent it out? Would we be able to get a joint mortgage together if the house had a tenant? We don't earn fantastic salaries but could certainly afford a house together. Any help, advise or pointers would be appreciated... Thanks