Parsing and Tagging are very important tasks in Natural Language Processing. Parsing amounts to searching the correct combination of grammatical rules among those compatible with a given sentence. Tagging amounts to labeling each word in a sentence with its lexical category and, because many words belong to more than one lexical class, it turns out to be a disambiguation task. Because parsing and tagging are related tasks, its simultaneous resolution can improve the results of both of them. This work aims developing a multiobjective genetic program to perform simultaneously statistical parsing and tagging. It combines the statistical data about grammar rules and about tag sequences to guide the search of the best structure. Results show that any of the implemented multiobjective optimization models improve on the results obtained in the resolution of each problem separately.