Where does your sewer end and the council's begin?
With a blockage outside, that is the question that decides the bill. The honest answer: it differs per municipality.
If the blockage is indoors, it is your pipe and your bill. If it sits outside, somewhere between the façade and the street, things get more interesting — because a boundary runs there, and it does not lie in the same place everywhere.
Dutch urban-water knowledge centre Stichting RIONED names three logical boundary demarcations between private and public sewer: 50 cm from the building façade (the boundary between building and external drainage under NEN 3215), at or near the property boundary at the level of the access point, or all the way to the main sewer in the public road. Three different places, then, with three different answers to the question of who pays.
Which of the three applies to your home is not fixed nationally. Stichting RIONED describes that under the law the municipality is free to determine what belongs to the main sewer and where the house connection begins, and writes that the municipality can prevent disputes by setting this down in a by-law — including that the house connection is the homeowner's property. So before you call, look up your municipality's connection or sewer by-law; that is the document deciding your situation.
Practically: the access point is the thing to know. It is the hatch or cap on your plot where a pipe can be reached, and in many by-laws the boundary coincides with the property line there. If you do not know where it sits, a camera inspection (€ 85-175) maps the run of your house connection — useful before a discussion about the bill, not after. If there is a plug right now, clearing a blockage costs € 125-350; every rate is in the price index.