Personally, I wouldn't like to have 2 layers of underwear under my pants, yet to each his own. I ride a bike about 5,000 miles per year, both to commute to work and for sport. Lycra cycling shorts or bibs with a padded crotch is essential to handle extended periods on the seat. When I get off the bike, the last thing I want to wear is anything snug around my crotch. I was a briefs guy for decades and started to wear boxers 4 years ago. I like the looser fit better than the confinement of snug underwear.
My suggestion: Try wearing just one pair of underwear. Once you get used to it, you'll feel more comfortable.