Patients with Parkinson's disease (PD) often suffer from cognitive impairment and depression in addition to motor dysfunction. These non-motor symptoms may be challenging to diagnose and disentangle from the effects of motor impairment. Analysis of vocal acoustics may improve detection and differentiation of motor, cognitive, and depressive symptom domains simultaneously. Certain vocal markers may be distinctly correlated with specific symptom domains, while other vocal markers may overlap across domains. In this paper, a joint multi-domain characterization of PD symptoms is presented. Speech recordings from 35 PD patients were analyzed for speech markers characterizing articulatory coordination based on resonant (formant) frequencies and delta-mel cepstral coefficients (dMFCC), as well as phonemic timing based on phoneme-dependent speaking rates. Moderate correlations were found between vocal markers and the motor and cognitive symptoms of PD, and weaker correlations with depressive symptoms. Notable differences were identified in the correlation patterns for each symptom domain. Of particular interest, the durations of certain phonemes were correlated with cognitive compared with motor symptom severity. Statistical models, developed based on the vocal markers, achieved moderate accuracy in predicting motor severity (r=0.42) and global cognition (r=0.52) but not depression (r=-0.21). This work suggests it may be possible to distinguish the impact of non-motor PD symptoms on speech. Future study is warranted to further develop symptom-specific vocal marker models in PD.