Great question. I think we can all agree that Jesus would be an appropriate model to follow. The Gospels show us that Jesus prayed often to the Father, and even describe for us his physical posture. Sometimes he would kneel (Luke 22:41-43) or at times even lay completely prostrate (Matthew 26:39). But at other times Jesus would turn his face towards heaven (John 17:1). By looking towards heaven the implication is that he did not close his eyes (whether he closed his eyes when he was kneeling or laying prostrate in prayer we have no idea. Scripture never records anyone closing their eyes during prayer).
Psalm 123:1 says "To You I lift up my eyes, O You who are enthroned in the heavens". By turning his eyes upward Jesus was indicating the Father's majesty and authority. John Calvin said that "by looking towards heaven, we are reminded that the majesty of God is far exalted above all creatures. By contrast, when Jesus lay prostrate in prayer he was indicating his submission to God, and declaring how much he needed God's protection and strength.
The ultimate issue isn't one's physical posture. Rather, it is the attitude of the heart. I cannot read your husbands heart (or yours). If you both are striving to show reverence to the Lord and submit your lives to His will, then don't worry so much about whether or not he closes his eyes. If his heart is flippant, then no posture will fix this anyway.
You are both communicating to Abba, Father, the Creator of the Universe. Let your mind and heart be overjoyed by the awe of that great privilege.