Depending on country, this might not be entirely accurate.
Here, you could be held financially responsible for providing for a child your spouse have parental responsibility for through the financial contract that marriage is, but you do not have parental responsibility for the child through marriage. Unless you put your name on the birth certificate (only the person giving birth get their name on that automaticly), adopt, have a verdict from the correct government agency or have it court ordered.

So absolute worst case you can end up paying child support to your wife's boyfriend if he wins full custody and she is broke. But you'd still have no parental responsibility or any say in the child's life.