We use parsing as sequence labeling as a common framework to learn across constituency and dependency syntactic abstractions. To do so, we cast the problem as multitask learning (MTL). First, we show that adding a parsing paradigm as an auxiliary loss consistently improves the performance on the other paradigm. Secondly, we explore an MTL sequence labeling model that parses both representations, at almost no cost in terms of performance and speed. The results across the board show that on average MTL models with auxiliary losses for constituency parsing outperform single-task ones by 1.05 F1 points, and for dependency parsing by 0.62 UAS points.