During the biofilm life cycle, bacteria attach to a surface then reproduce, forming crowded, growing communities. As these colonies develop, they expand horizontally and vertically. This horizontal expansion, known as the range expansion, occurs at a constant rate, which is often used as a proxy for bacterial fitness. Conversely, the vertical growth of biofilms is much less studied, despite representing a fundamental aspect of bacterial physiology. Many theoretical models of vertical growth dynamics have been proposed; however, difficulties in measuring biofilm height accurately across relevant time and length scales have prevented testing these models or their biophysical underpinnings empirically. Using white light interferometry, we measure the heights of microbial colonies with nanometer precision from inoculation (sub-micron) to their final equilibrium height (hundreds of microns), producing a novel and detailed empirical characterization of vertical growth dynamics. We show that models relying on logistic growth or nutrient depletion fail to capture biofilm height dynamics on short and long time scales. Our empirical results support a simple model inspired by the fact that biofilms only interact with the environment through their interfaces. This interface model captures the growth dynamics from short to long time scales (10 minutes to 14 days) of diverse microorganisms, including prokaryotes like gram-negative and gram-positive bacteria and eukaryotes like aerobic and anaerobic yeast. This model provides heuristic value, highlighting the biophysical constraints that limit vertical growth as well as establishing a quantitative model for biofilm development.