This work visits the topic of jointly parsing constituency and dependency trees, i.e., to produce compatible constituency and dependency trees simultaneously for input sentences, which is attractive considering that the two types of trees are complementary in representing syntax. Compared with previous works, we make progress in four aspects: (1) adopting a much more efficient decoding algorithm, (2) exploring joint modeling at the training phase, instead of only at the inference phase, (3) proposing high-order scoring components for constituent-dependency interaction, (4) gaining more insights via in-depth experiments and analysis.