First, you can rule out the idea that Dante "believes in" the Greek gods.
Dante's vision of hell in the Inferno is not intended to be literal. He wrote poetry, not theology. The poem is allegorical on several levels. That means he uses people, places, and things more for their representational value than for what they are in themselves. In other words, Cerberus and the Minotaur, etc. aren't real. They are a device used to communicate something about the nature of hell.
Remember, this is a poem in the classical tradition. It's essentially an epic poem, which requires certain conventions, including references to mythology. He uses these references to create an overtly Christian story. Just like Milton and Spenser and even like C.S. Lewis and J.R.R. Tolkein.
The Divine Comedy is the story of Redemption--a journey through hell, purgatory (Catholic, remember), and finally heaven. Dante borrows from the classic tradition and uses their characters and devices and uses them for a God-honoring purpose.