We present a parsing model for projective dependency trees which takes advantage of the existence of complementary dependency annotations for a language. This is the case for Arabic with the availability of CATiB and UD treebanks. Our system performs syntactic parsing according to both annotation types jointly as a sequence of arc-creating operations following the Easy-First approach, and partially created trees for one annotation type are also available to the other as features for the score function. This method gives error reduction of 9.9% on CATiB and 6.1% on UD compared to a single-task baseline, and ablation tests show that the main contribution of this reduction is given by sharing tree representation between tasks, and not simply sharing BiLSTM layers as is usually performed in NLP multitask systems.