In my house I have it lit with shroom light but mobs are spawning inside of it (the screenshots are the rooms I've seen mobs spawn in so far)
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Your rooms are not adequately lit. For example, in the chicken room, for example, the spot directly in the center is at light level 7. Soul lanterns and soul torches are light level 10, and the lantern is 4 blocks up, so you count down 10 - 9 - 8 - 7. The shroomlights in the corners of the floor are level 15, so the space above them is at 14, and counting by 2's diagonally they would only make the center block level 6.
In the room with shroomlights hanging from chains, they space above the floor directly under each one is at light level 10, so there are several blocks diagonally in between them that are spawnable.
For more information on calculating light levels see the Minecraft wiki. You may find it helpful to temporarily turn off smooth lighting (in video settings) to see how the light levels change block by block.
This ticket will be resolved as a duplicate of MCPE-302.
Could you include a screenshot of the inside of your house?