From the Now Playing screen/full player view: Tap the "X" to exit the Full Player view. Now, you are able to go to shows in your playlists, or search or browse for shows while still listening to a different podcast. To see available episodes:
From Search or Browse: Tap the magnifying glass icon in the top left. Once you are viewing a list of shows, click on the show image or show name to view the episodes available within that particular podcast. You can play any of the listed episodes by tapping it.
From your playlists: Tap on a playlist, then on the show you’re interested in. Click the list icon to view the episodes available within that particular podcast.