Being married to an unbeliever can be frustrating and discouraging. You’re pulling one way. He’s pulling another. You make decisions based on your faith and trust in God. He thinks only of himself. Ugh.
There is hope, but your situation may not change overnight. The key is persistent prayer. One wife, whom I know quite well, prayed earnestly for about 15 years before her husband finally came to Christ. It was discouraging at times, but she kept believing that God would answer her prayer, and He did. It just took time (15 years!) for God to soften her husband’s heart.
May I suggest that you pray Ezekiel 36:26-27 every day for your husband, inserting his name in the verse? The verse talks about God turning a heart of stone into a heart of flesh. In other words, God can soften hard hearts! Here is how you might want to pray this verse: “Jesus, give (insert your husband’s name) a new heart and put a new spirit in him. Jesus, remove (insert name)’s heart of stone and give him a heart of flesh. Jesus, put your Spirit in (insert name) and move him to follow your decrees and be careful to keep your laws.”
Also, to encourage yourself to keep diligently praying and trusting God, you may want to read the parable of the persistent widow in Luke 18.