How to know if my ancestor's mother was his biological mom on census?

A birth certificate if within the dates of birth registration, you pay and apply for it and that will names both his parents

A census will not show this.............only a Birth Certificate show this information.

A DNA test. If she had a fling with a guy who generally resembled her husband, but never told, the hubby would go on the birth certificate.

If you can find a birth certificate for your answer this should list both mother and father; the listing for mother is likely to be more accurate than for the father.

Just because the father's family came from England (I'm assuming you're in the US?) doesn't mean they won't have had any dark skinned ancestry, there have been dark-skinned residents of the British Isles for 2000 years or more. Your ancestor may be a 'throwback' (not sure what a more politically correct modern term would be), someone whose appearance is more influenced by genetics from further back in their ancestry.

1. Look for a birth record.

2. DNA test one of his descendants against a descendant of a known biological child.