Cyclocross suspension
While proper cyclocross bikes typically do not have front suspension, you can find a few drop-bar bikes that do have it.  The Cannondale Slate is one: http://www.cannondale.com/en/USA/Bike/ProductDetail?Id=4a8a930f-c1de-422f-bf23-81d13da8c706

These bikes are usually called "adventure bikes."  While most adventure bikes still don't have suspension, the term may help you narrow your search.

You may find that a good quality, wide front tire is enough suspension.  Any drop-bar bike with clearance for tires at least 40mm wide should be useful here.  This opens your options up to a much bigger slice of the adventure bike market.