I'm on H1B that I want to keep, but I'm about to co-found a start-up

I don't want to risk my H1B and current job at all. I currently work at a fortune 500 company and it's a really nice deal.

However, I helped build this great website which will be an automated business (memberships based). I'm going to be a passive owner with 15% share in this business (a LLC). I'm not planning on to receive any salary or put any active work in the business.

Is there any way I'm jeopardizing my current H1B visa, or might this later create problems on the way to a Green Card?

You should talk to an attorney. Generally, partner's income is considered self-employment income. From tax perspective, you'll be earning money from self-employment. Since its an LLC - you cannot be a limited (passive) partner or shareholder (there are no shares in LLC), you're a member.

I'm not a lawyer, so verify with a professional, but I do think that you're jeopardizing your H1b and future immigration/naturalization proceedings.

If you want to be a passive shareholder, consider incorporating as a C-corporation. That's the only entity which allows you being a real passive shareholder (all the publicly traded corporations are of this kind). You'll be able to hold the shares and maybe (ask a lawyer) be a board member of such a corporation.

Is there any way I'm jeopardizing my current H1B visa, or might this later create problems on the way to a Green Card?

Yes, you ARE jeopardizing your current status and this will likely become an issue when it gets to getting your green card. Your H-1b status allows you to work only for your current company and nobody else. You are currently working for another LLC and it will be recorded on your taxes, etc. Especially if you used your SSN. I'd definitely talk to a lawyer ASAP.