Your H being comfortable with you around his parents is a huge sign that things are progressing nicely. Another thing of huge importance is that H spent time away with you in the kitchen while his parents stayed on the patio with your D, this sent them a message that you two are reconnecting...IMO, H wanted them to see just that. He would not have paid as much single attention to you if he didn't. IMO, he would have treated you less warmly in front of them. He sent this message to them because he wanted them to see your progress!!!
It will be interesting to hear MIL's perspective. MIL and FIL are coming to dinner tonight when H is working.