H-1B professionals do not require Advance Parole to travel abroad while an adjustment application is pending based on marriage to a US CItizen or a Green Card holder. They can re-enter the U.S. with a valid H-1B visa without jeopardizing their status.

Departing the U.S. before an Advance Parole document is granted will result in the abandonment and automatic denial of the pending I-131 application if you have a marriage-based Adjustment of Status pending unless you have a valid H-1B stamp.