In this paper, we examine the problem of visibility-aware robot navigation among movable obstacles (VANAMO). A variant of the well-known NAMO robotic planning problem, VANAMO puts additional visibility constraints on robot motion and object movability. This new problem formulation lifts the restrictive assumption that the map is fully visible and the object positions are fully known. We provide a formal definition of the VANAMO problem and propose the Look and Manipulate Backchaining (LAMB) algorithm for solving such problems. Lamb has a simple vision-based interface that makes it more easily transferable to real-world robot applications and scales to the large 3D environments. To evaluate Lamb, we construct a set of tasks that illustrate the complex interplay between visibility and object movability that can arise in mobile base manipulation problems in unknown environments. We show that Lamb outperforms NAMO and visibility-aware motion planning approaches as well as simple combinations of them on complex manipulation problems with partial observability.