Is celebrating the birth of the Prophet (SAW) a sinful bidah?

I'm a convert, but follow mostly Sunni teachings from Hanafi or Maliki. I'm wondering if celebrating the birth of the Prophet (SAW) is bidah, and thus a sin. My husband thinks so, but he tends to lean highly conservative. I'm of the opinion that it may be innovation, but it's harmless, and just brings the family together for a day of joy. I'm looking for someone to give me hard facts, and prove if it's a harmful bidah or not. I'm aware that taraweeh prayers are technically bidah, and I have heard that Umar praised them as a "beautiful bidah," although I'm at the moment unable to validate this claim. So, if there can be a bidah that's harmless, and even praised and encouraged, then how can all bidah be harmful, and is the celebrating the Prophet's birthday really so bad?