Yes, in most cases they can, as long as the suppliers behind each part are connected to your portal and your plan includes combined selling. The customer searches, picks a flight and a room, and reaches one basket with one payment screen, so they enter their traveller details and card details once and get a single confirmation for the trip.
Behind the scenes they are still two bookings with two different suppliers. Your portal simply joins them together and presents them as one trip. What you can bundle depends on which suppliers you have live, what each supplier's API allows, and what you have switched on. Some hotel suppliers are perfectly happy to sit inside a package, others will only sell on their own, and flights are usually the part that limits you because seat availability moves the fastest. So this is something to confirm supplier by supplier rather than assume across the board.
It also helps to remember that the rules of each part stay separate even when the price is shown as one. If your customer cancels, the airline fare rules apply to the flight and the hotel rules apply to the room, so one basket does not mean one cancellation policy. The same goes for date changes, and your customer will normally receive a ticket for the flight and a voucher for the hotel rather than one document. Showing both sets of conditions before the payment page saves a lot of arguments later.
The sensible next step is to list the suppliers you already have and ask which of them permit combined selling, then decide whether you want your website to promote a package saving or just the convenience of booking once.