Unbelief probably has many more than three faces, but I see these clearly lurking in my heart.
1) Independence. I choose not to believe in God's power or goodness because I don't need to. Who needs God when I have myself? Who needs the gifts God gives through people, leaders, counsel, encouragement, or correction, when I have my own thoughts to keep me company?
2) Fatalism. All that happens would have happened whether I prayed or not, whether I obeyed or not, whether I believed God or not. Since God is sovereign over all things, I'll just do what I want and walk through life experiencing the pain and joys I was always meant to experience.
3) Cynicism. Even my best efforts are unworthy, so God is probably looking for new ways to punish me. I may pray, but God will not listen. I may obey, but God will not be pleased. I may trust, but God's anger will get me in the end.
All three of these faces turn away from the invitation of faith. Faith says:
1) Trust. I am dependent on God for all things. I need the people he has placed in my life. I am glad to feel weak so that he can demonstrate his power through me. I trust the all-powerful God.
2) Trust. I will pray and obey without understanding how a Sovereign God can "respond" to prayers, or be pleased with a choice he ordained me to make. I don't need to know how prayer, obedience, and sovereignty are reconciled. I trust the all-wise God.
3) Trust. I am unworthy, but God sees me in Christ. I may fail, but God will use even my failures for my good and his glory. I will stumble, but God will preserve me till the end and will present me blameless in the day of Christ Jesus. I will trust the all-good God.
The faces of unbelief mask a heart that doubts the character of God. The heart of faith finds God's character an endless source of wonder and confidence, fully worthy of our trust.