It's ironic you phrase the question this way, since this is exactly what we believe: We believe that everytime we partake of the Eucharist, in the form of bread, that we actually receive both the Body and the Blood. So we actually do receive both, even if we only receive the consecrated Host.
As for your question regarding unleavened/leavened bread used in the consecration, it's an interesting one, one I recently heard myself. I don't know the answer although I think Mad Dawg may be onto something. Perhaps our Orthodox bretheren could shed some light on it though.
Because partaking in the host is taking in Christ in whole. Why bother having any wine at all?