Character-level models have become a popular approach specially for their accessibility and ability to handle unseen data. However, little is known on their ability to reveal the underlying morphological structure of a word, which is a crucial skill for high-level semantic analysis tasks, such as semantic role labeling (SRL). In this work, we train various types of SRL models that use word, character and morphology level information and analyze how performance of characters compare to words and morphology for several languages. We conduct an in-depth error analysis for each morphological typology and analyze the strengths and limitations of character-level models that relate to out-of-domain data, training data size, long range dependencies and model complexity. Our exhaustive analyses shed light on important characteristics of character-level models and their semantic capability.