I wanted to keep it short, as it is a really basic question with an easy answer, but after reading comments I'll expand it a bit.
To enter the Schengen area you need a travel document for you next destination, valid for at least 90 days after the day you plan to leave; this is by law, so you have no options around this.
Your only option is to get a US Visa extension.
I tried to quote those here, but honestly it take too much. For all who needs to better understand things just read them, is just a couple of hours and fully understandable.
Basic points are:
- To be allowed to enter Schengen area you must demonstrate be able to sustain yourself while there (ok, just ignore this)
- To be allowed to enter Schengen area you must demonstrate to have the right to stay here indefinitely or to be able to exit from it. Notice: exiting, not just going back to starting the point. You just need to demonstrate that you can reach your next destination, whatever it may be.
- You are an US immigrant, not an US resident, thus your passport should not have been issued by US government but from the government of the nation you reside. Your passport is always valid to enter your nation of residence
- As you are an alien, your actual passport is not a valid document per-se stating that you can enter USA
- You have an I permit, that allow you only to stay in US
- You have an I permit, that do not grant you the right to enter US
- You have a Visa allowing you to enter USA from a POE (Point of Entry)
- The above are NOT LINKED, you can have one without the other, they serve different purposes.
- As for your flight tickets, you are leaving from USA and affirming you will be going back to USA. Thus you need to demonstrate you will be able to reenteR USA
- For leaving USA you need a valid passport and to reenter you need it, too. Passport scope is simply to certify your identity internationally, it has no other function per se.
- To enter USA you need a valid document attesting you can actually do it. Your Visa is enough, and it is still valid, so this is ok.
- To enter Schengen, you need to testify that you will be able to still enter USA after three months of the date of the intended departure:
From the first link above:
The applicant shall present a valid travel document satisfying the following criteria:
its validity shall extend at least three months after the intended date of departure from the territory of the Member States or, in the case of several visits, after the last intended date of departure from the territory of the Member States. However, in a justified case of emergency, this obligation may be waived;
Again, your passport per se is not a valid document to reenter the USA, as you are an alien. But your passport with an US Visa on, it is.
So, for your passport to be a document whose validity extend at least three months after the intended date of departure from the territory of the Member States it must have a Visa on it valid three months after the intended date of departure etc. etc. etc.
So, again, to solve your problem you need an extension to your US Visa. How to do that or if it is possible...well, I honestly don't know.