Coffee does contain oils that will "increase cholesterol" (meaning increase LDL/bad cholesterol specifically). Filters reduce the oil significantly but unfiltered methods like cafetière and espresso (which is the basis of cappuccino etc) let it all through. It's something to think about if your drinking many unfiltered coffees a day. It is possible to add a filter to espresso if you brew it yourself.
> Cafestol, a diterpene present in unfiltered coffee brews such as Scandinavian boiled, Turkish, and cafetière coffee, is the most potent cholesterol-elevating compound known in the human diet.