Meanwhile in the TARDIS (home video)

Meanwhile in the TARDIS is a title which describes two mini-scenes set during Series 5 of Doctor Who, which were made available on the Blu-Ray and DVD releases of that series.

First Episode
The first episode of the series was: The Eleventh Hour. This episode was mainly composed of the usual "companion-first-starting-out" questions. Amy asked the Doctor questions about how the TARDIS retains its air supply if it's made of wood, why it's a police box, why the Doctor looks human, etc.

He finally showed her that they were in space. Amy comments that it looked like special effects in a studio, so the Doctor proved it was real by pushing her out of the TARDIS. This action is the starting point of the next episode The Beast Below, which starts with Amy hanging out of the TARDIS in space

Second episode
The second bridged Flesh and Stone and The Vampires of Venice. The episode directly continued after Amy's seduction attempts on the Doctor. She went right into the TARDIS while the Doctor ignored her for a minute, She then started to talk about how she's getting "mixed messages" about his taking her with him in the TARDIS. He eventually tells her that he doesn't "see it". He starts to explain that making space your "backyard" for 907 years, everything just becomes "stuff" but that she can see it. She ignores that theory and wonders if there were other companions. He responds very shyly and says "some, maybe a few....". She asks if she could see the visual records. The Doctor explains that they're "voice locked". So Amy tries to open them by saying a command. The Doctor corrects her by explaining that a voice lock only responds to his voice while inadvertently saying the command, allowing Amy to see pictures of all his past companions. When Amy starts making fun of him about all of his companions (especially Leela), he decides that it's time to get Rory, leading into the beginning of Vampires in Venice.