Recently, powerful new observations and advances in computation and visualization have led to a revolution in our understanding of the structure of the Universe. As the field of cosmology advances, it is of interest to study how student ideas relate to scientific understanding. In this paper, we examine in-depth undergraduate students' ideas on distances and structure in the Universe as students progress through a general education astronomy integrated lecture and laboratory course with a focus on active learning. The study was conducted over five semesters at an urban, minority-serving institution. The data collected include individual interviews (N = 15) and course artifacts (N [approximately] 60), such as precourse homework essays, prelab surveys, and midterm and final exam questions in a variety of formats. We find that students are fairly successful at tasks involving relative distances, but struggle with absolute distances; have difficulty going beyond an elementary model of the Solar System as the Sun and planets; struggle to visualize galactic halos; but successfully increase their understanding of the hierarchical nature of structure in the Universe throughout the semester. (Contains 66 tables, 13 figures and 6 footnotes.)