いえ means buildings like house or apartment. うち includes いえ.
いえ is used when you want to mention a place or a person close to you.
If you want to invite your friends to your house. Using うち sounds natural and welcoming. いえ is good, but うち is better I think.
うち is a usuful word peculiar to Japanese.
・うち に かえる → go home
・うち の おかあさん → my mom
・うち の CEO → our CEO
・うち は 24じかん やっています
→ we open 24 hrs.
I think mostly you can replace いえ with うち.