I think you are confusing some things. PMI stands for principle mortgage insurance. That is a fee/insurance you pay each month (included in your mortgage payment) when you owe more than 80% of what the home is worth.
I think your question is how do you purchase a NEW home when you don't have the 20% down payment to get a typical conventional loan.
It really depends on what kind of home construction you are doing.
If you plan on building a custom home, a draw system is commonly used (the foundation is put in and the bank gives you the money to pay for it, then the framing is done and the bank gives you the money...etc). This is a risky loan since the bank is lending you the money in allotments and the risk is whether or not the house will be fully completed and worth all the money lent to build it.
If you wait on the mortgage until after the home is finished (the builder holds the note or you buy into a development where they build it you buy it), you have many more financing options. It is possible you could do an FHA Loan with only 3.5% down.
The rules are changing every day. You should consult with a local mortgage rep to determine exactly what options you have based on what you are trying to do.
Long & Foster Real Estate, Inc
Lehigh Valley Office, PA