I think you are. In fact, it would still be the case if you were married. The Schengen regulations contain many provisions regarding members of the family of EU citizens (relaxed requirements to obtain a visa, whether their passport need to be stamped, etc.) but no clear exemption from the maximum stay rule.
What your relationship allows (with some caveat for de facto relationships and without conditions for married couples) is taking up residence in any EU and/or Schengen country. But as long as you don't secure a residence card, the 90-day rule applies.
On a purely theoretical level, you could try to argue that this curtails your partner's right of free movement but it seems that in practice the current state of the law does restrict the length of your stays in the Schengen area.
Importantly, article 10 of the Schengen Borders Code provides that:
- The travel documents of nationals of third countries who are members of the family of a Union citizen to whom Directive 2004/38/EC applies, but who do not present the residence card provided for in that Directive, shall be stamped on entry and exit.
- No entry or exit stamp shall be affixed:
(g) to the travel documents of nationals of third countries who present a residence card provided for in Directive 2004/38/EC.
Stamping only makes sense to check if a person abided by the maximum stay rule and the regulation clearly makes a distinction between third-country nationals who enjoy the right of free movement (“to whom Directive 2004/38/EC applies“) but do not have an actual residence card and those who do.
Similarly, holders of long-stay visas or residence permits in a Schengen country (including members of the family of an EU citizen or youth-mobility/work-holiday visa holders) are only entitled to travel to other Schengen countries for 90 days in any 180-day period. In practice, enforcement is difficult and limited but the logic of the system is clear: You can only take up residence in one country and visit others for a short time, not travel indefinitely in the whole area without any formality.
Another subtlety is that directive 2004/38/EC specifies in many places that failure to comply with one obligation or another should only result in “proportionate and non-discriminatory sanctions“. What is implied here is that overstaying could make you liable for a fine but should not result in detention, deportation or a ban. So there are some rules and restrictions on stays longer than three months but you are in principle protected from some of the most serious consequences of breaking them.