Is it permissible to combine the Dhuhr and Asr prayers by delaying them (jama' ta'kheer) and shortening them to two rak'ahs each, while traveling, upon arrival and departure, after the Adhan for Dhuhr and Asr?

What you did is correct if your travel was permissible, and there was nothing to interrupt the journey, such as having a wife whom you have consummated with in the town, or an intention to reside for four days or more, excluding the days of entry and departure, or if the town is your homeland. Merely owning a house in the town does not interrupt the ruling of travel; rather, the determining factor is whether it is your homeland. You are permitted to begin shortening and combining prayers after passing the inhabited houses of your village.