You were experiencing what is called by us speech-language development folks as "simultaneous language acquisition." There are often imbalances in both the amount of exposure to the different languages, and the quality of the exposure to the different languages:
Simultaneous Language Acquisition: parental input
You can indeed be considered to be natively bilingual in more than one language. When children are exposed to multiple languages from birth, there may be cross-language usage very early in development, and there may be mild delays (compared to development of children in monolingual environments). This is a great article from the American Speech-Language Hearing Association about bilingual language acquisition> it is geared towards laypeople who have an interest in or concern about bilingual language acquisition.
ASHA Bilingual Language Acquisition info page
It sounds, though, that perhaps you're more proficient in English, and can absolutely be considered a native speaker of English, since you were exposed to it from birth and throughout the critical period of language development.