Reading literacy is a multidimensional construct in terms of text and reading processes. Much research has examined the divisibility of the processes underlying reading, but they have treated the rest of the construct as unitary. This study extends the examination of dimensionality to a neglected area in literacy studies. It tests reading models by integrating text formats (continuous, mixed, and non-continuous) and cognitive processes involved in reading (information retrieval, interpretation, and reflection) and their interaction in a large dataset. The study aims to complement the results of previous research by analyzing how cognitive aspects function in the meaning-making process in various text formats. Representative samples (N = 3229) of young Hungarian L1 learners participated in the study. Data obtained from a longitudinal study in grade 2 and grade 4 is used to test the underlying measurement model of reading literacy and to explore the issue of the dimensionality of reading processes along three different text formats. Findings suggest that students' reading development trajectory and rate differs when it comes to reading texts with different formats. Text formats affect reading subskills significantly but the interaction between text and reading processes changes over time. Results provide a clearer understanding of the text format achievement gap. Implications for research and practice are discussed.