rather than drilling 3/8" holes I would consider getting some Joist Hangers from your local lumber yard or Lows, Home Depot, etc. You can afix them to the frame with only self tapping screws. They are designed to carry the weight and you do not risk weakening your frame by drilling holes.
If you MUST drill holes, Id use 1/4" instead and be sure to drill in the center of the frame member so as not to weaken it in either tension of compression when it flexes under a load.
2013 Wildcat Sterling 32RL
2008 Chevy Silverado 2500HD LT Diesel
2001 Cougar 281 EFS (sold)
1973 Layton 23' (sold)