Riding a bike on a tilted road I have a dutch city bike (similar to the one shown below) with broad tires that I use for commuting short distances. When traveling on roads with a slight tilt (left to right, perpendicular to the road), I often find myself feeling unbalanced, as if tilt of the road is exerting a force on my tires, pushing me against the tilt.

What am I doing wrong? Can something be wrong with the bike/tires or is it just "me"?
If you feel no "tilt" on a flat road then there is probably nothing wrong.  A bike's steering geometry is designed as a compromise, using terms such as "rake", "head angle", and "trail".  A bike designed for agility will generally have a geometry that makes it turn downhill on a slope (if you let go of the handlebar), but a bike designed for stability (such as yours) will tend to turn uphill.  This tendency is amplified by the wider, lower pressure tires.  

I doubt that there is anything wrong with the bike, unless this effect is very pronounced.

If you find the effect unsettling you might be able to reduce it by increasing your front tire pressure 20-30%.