If that entity is owned by your spouse, it can be an issue for H1B sponsorship.
Why would it matter who owns the sponsoring firm? As long as all H-1B regulations are being met, I see no issues, unless I a missing something here.
I am on H1b, my GC is in process. Would there be any problem to get GC if I marry my employer?
While H1B sponsorship by a company owned by oneself or one's family is allowed, there will be additional scrutiny involved. Employment-based sponsorship for a green card in such a situation is much more restricted.
Yeah I don't see what's the issue either. As long as the Employer files the petition for employee and follows the guidelines and procedure, which they did hence the H1B is granted. Now, the romance fires up at work and they want to get married. What's wrong with that?