I mean just in case questioned by the boarder patrol because I don't have receipts yet from the USCIS. I am still AOS. Thanks
Not without risk.
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Just to be on the safe side, I would wait until a receipt notice is received from USCIS. Having a marriage certificate doesn't necessarily prove that you have an application pending.
Generally speaking, traveling within the US shouldn't be a problem. However, if you need to use your foreign passport as proof of ID because you don't have a valid driver's license, then that could trigger a DHS officer to inquire about your immigration status. If you are a visa overstay, for example, that would mean that you are in the country unlawfully. Having the receipt notice would be more acceptable proof (in my opinion) that you are doing what you must to resolve that issue. Good luck.
[This answer is for general purposes only; it does not constitute advice and does not establish an attorney-client relationship.]
Neither the I-130 or I-485 are travel documents. Your I-131 is your travel document, which will take 60-90 days to be approved as long as it was properly filed. The travel document is meant for international travel, not domestic travel.
You do not need special documentation to travel domestically in the US.
However if you are not in a legal status not (and no pending Adjustment of Status is not a Legal Status), you may be detained or questions by immigration authorities and even placed into removal.
You should consult with an attorney to reverse engineer what you have done so that they can help you understand the what your status is and what you can do while on it, i.e. travel, work, etc.
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And foreign passport
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