Top of a convertible vehicle, comprising a headliner assembly

A top of a convertible vehicle, including a top linkage which can be displaced between a closed and a storage position has a linkage assembly on either side of a vertical longitudinal center plane. Each linkage assembly includes a main multi-bar assembly, which is pivotably mounted on a respective vehicle-attached main bearing, and a front roof link, which pivots relative to the main multi-bar assembly when the linkage assembly is actuated, and is covered with a headliner assembly when the top linkage is in the closed position. The headliner assemblies comprise a front headliner flap which is articulated to the respective front roof link via a link assembly and which can be pivoted between a covering and an uncovering position, in which the front headliner flap is located when the top linkage is in the storage position and in which the respective front roof link is accessible from above.