A multi-member LLC cannot file its tax return on a Schedule C. It can only file on a 1065 partnership return or a corporate return. S corp status is not available to foreign nationals.
I'm not an expert on immigration or visa status, but I believe an H1B visa holder can only work for the sponsoring organization, not anywhere they like. So anything that smacks of self-employment might cause visa problems. Partnership income is typically considered self-employment income. You can certainly invest. The best avenue would seem to me to be a C corporation and hiring someone else to run it.

