Is There Such a Thing as Perfect Faith?

For years, I've thought that I was a woman of faith--someone who could believe God, despite the circumstances.  But recent events have left me questioning my faith and my understanding of faith.

In Scripture, we see people doubting God's promises, but God still fulfilling those promises. We see this in the lives of Abram, Sarai, and Zacharias.  They doubted, but God still did what He promised.  But in the book of Mark, we see Jesus not doing miracles because of people's lack of faith.  And throughout the New Testament, we see exhortations to have faith and not doubt.

This leads me to wonder what exactly having faith means.  Is it the total absence of doubt?  Or is it overall trust in God, even if doubt creeps in sometimes?

I'm realizing that I've spent years trying to exercise a faith that is perfect, fearing what would happen if I didn't. 

Now my understanding of faith is changing.  I no longer think that my faith must be perfect.  Rather, I think that faith involves my taking my moments of doubt to God, and asking Him to speak into those doubts with His truth, and love, and grace.  I'm starting to think that the act of my taking myself (and fears and doubts) to God may be the only type of faith that God has ever asked me to have.