Same bank holds mortgages on two properties? what will happen?

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I have two properties with two mortages each. The 2nd mortage on the 1st property is held by the same bank which holds BOTH mortages on the 2nd property.

Property 1
1st Mortage - Bank A
2nd Mortage - Bank B

Property 2
1st Mortage - Bank B
2nd Mortage - Bank B

If I file Chapter 7 and want to keep Property 2, what would happen? Bank B would have lost out on the first property but still hold mortages on the second property I intend to keep. Is this possible to pull off?