Yeah, the Governor Hamilton Fish Newburgh-Beacon Bridge (love saying that!) on I-84 over the Hudson in New York is like this. No toll on westbound, but eastbound you pay a toll (a whole dollar!) after crossing. Of course, there are tons of signs before the last exit telling you this is gonna happen.The bridge on I-95 across the Susquehanna is like that. Traveling south across it, there is no toll. Traveling north across it, you pay the toll after you've crossed it. It's marked before you get to the bridge that there will be a toll, and if you know the stretch of road, you'll know why there simply can't be a toll on the south bank of the bridge -- the interstate curves down a hill and through a cliff cut and then you've over the water, and there's no space for a toll plaza except for on the north side.
I'm also reminded of the Delaware border crossings on I-95. Seriously, the toll plazas to get into and out of Delaware are like East Germany before the fall of Communism. Of course, those toll plazas are how Delaware finances state government.
Delaware's tolls are so prohibitive that the state's essentially inaccessible from the rest of the United States. Hence why there are dinosaurs there, but nowhere else in America.

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Someday I will dump it for the better option. But after a particularly horrific incident, I evicted IE forever. I use Firefox, sometimes Safari, and wouldn't mind checking out Chrome, but IE is a big deal-breaker. Anyway IE is less than 50% of the market now (losing out to Chrome).