How can I travel overseas with an EAD/AP card?

If you get a new H-1B visa while abroad, you have a choice of returning on your H-1B or returning using the advance parole and work card.

You use the EAD/AP combo card at the port of entry and do not need a new visa. If you just work for the H-1B employer you may file for an H extension if necessary; otherwise, a new H would need to be consular processed if necessary. You may also work with the EAD including for the H employer, check with the employer on any I-9 update required.

Yes, you can travel with your AP card and when you return to the U.S. on the AP card, you will be admitted as AOS pending status. If you want to be admitted as H-1B, get a new visa while abroad.

Yes, you can travel overseas with your EAD/AP. However, the EAD/AP does not necessarily terminate the H-1B visa, but if your I-485 is approved your new conditional permanent residency would render your H-1B unnecessary as it essentially replaces the H-1b.

You can use the EAD/AP card to travel internationally. Just present the card along with your passport. When you re-enter on the EAD/AP, you will now be authorized for employment based on the EAD and pending adjustment of status.

Before traveling, be sure to have a visit with your investment immigration attorney. Generally, the purpose of advanced parole is to allow you to travel internationally while your adjustment of status application is pending.

The advance parole part is your permission to travel. H-1b is a dual intent status so you can keep the H-1b even if pursuing the green card. That said, I would either use one or the other to travel, not both.