We consider representations of non-negative integers in positional numeration systems, and study the question of the regularity of the generated numeration language, that is, the set of all greedy representations. In 1998, Hollander gave a precise description of dominant root positional numeration systems with a regular numeration language. Getting rid of the dominant root constraint, we provide a full and effective characterization of positional numeration systems leading to a regular numeration language. In doing so, we show that this framework gives rise to multi-base numeration systems for representing real numbers in a natural way. These systems were called alternate bases since they use a fixed number of real bases in an alternating way. This generalizes the well-known link between the dominant root positional numeration systems for representing integers and beta-expansions of real numbers. Our characterization of regular numeration languages also fills a gap left in Hollander's description for dominant root systems.