The latest developments in neural semantic role labeling (SRL), including both dependency and span representation formalisms, have shown great performance improvements. Although the two styles share many similarities in linguistic meaning and computation, most previous studies focus on a single style. In this paper, we define a new cross-style semantic role label convention and propose a new cross-style joint optimization model designed according to the linguistic meaning of semantic role, which provides an agreed way to make the results of two styles more comparable and let both types of SRL enjoy their natural connection on both linguistics and computation. Our model learns a general semantic argument structure and is capable of outputting optional style alone. Additionally, we propose a syntax aided method to enhance the learning of both dependency and span representations uniformly. Experiments show that the proposed methods are effective on both span (CoNLL-2005) and dependency (CoNLL-2009) SRL benchmarks.