Kenage na Niizuma ga, Hoka no Otoko ni Kiss Houshi Shimasu.

Weeks into their marriage, Anna Yuzuki is already cheating on her husband.

It's not her fault. After the honeymoon a man suddenly shows up.
He's Natsuki, an old friend of her husband, come to collect a large debt.

Seems that Anna's husband owes $100,000 dollars.

The husband is humiliated. He never wanted Anna to be involved in this.
"Maybe we should get divorced," he says. "Save yourself."
But she agreed to love him until death, for better or worse.

The friend, Natsuki, is a reasonable friend with a proposal that might suit everyone.

[From DLsite English]