Upvote:2
You can not connect Air Asia flights and Thai Airways flights on a single booking nor a single check in. But there is nothing really preventing you from using two separate bookings for a trip.
Air Asia is a point to point carrier, flying people only on their own aircraft. They do offer "FlyThru", which connects bags on some international routes, but that is ONLY Air Asia to Air Asia, not Air Asia to another carrier.
And flying through Bangkok means two different airports, as Air Asia flies via the older Don Muang Airport and Thai from the main Suvarnabhumi Airport. So in both directions you will need to clear immigration, claim your bags, clear customs, transfer by bus or taxi between the airports and check in for your next flight.
Whether you need a visa or can enter under the Visa Exempt program depends on your citizenship.