It sounds to me like you are describing a murabahah contract. These are generally considered acceptable in Islam so long as the following conditions are met:
- The final price is agreed upon by both parties at the time of transaction
- The final price does not change after the agreement is made (i.e. it doesn't increase in case of late payments)
- The bank first acquires the goods in full to sell back to you
From your description, this third point is the one I would worry about; if they're just giving you a loan of $180,000, and expecting you to pay back $380,000, that's a like-for-like transaction which is generally considered riba according to the well-known sayings of the Prophet e.g.:
Do not sell gold for gold, except like for like, and don't increase something of it upon something; and don't sell silver unless like for like, and don't increase some thing of it upon something, and do not sell for ready money something to be given later.
— Sahih Muslim 1584a
However, if the contract involves them agreeing to purchase the home with $180,000 such that the home is now in their name and they can sell it as they wish, and then you buying that home back from them for $380,000, that is considered a regular trade agreement in which profit is acceptable.