We study the layered J(1)-J(2) classical Heisenberg model on the square lattice using a self-consistent bond theory. We derive the phase diagram for fixed J(1) as a function of temperature T, J(2), and interplane coupling J(z). Broad regions of (anti)ferromagnetic and stripe order are found, and are separated by a first-order transition near J(2) approximate to 0.5 (in units of vertical bar J(1)vertical bar). Within the stripe phase the magnetic and vestigial nematic transitions occur simultaneously in first-order fashion for strong J(z). For weaker J(z), there is in addition, for J(2)* < J(2) < J(2)**, an intermediate regime of split transitions implying a finite temperature region with nematic order but no long-range stripe magnetic order. In this split regime, the order of the transitions depends sensitively on the deviation from J(2)* and J(2)**, with split second-order transitions predominating for J(2)* << J(2) << J(2)**. We find that the value of J(2)* depends weakly on the interplane coupling and is just slightly larger than 0.5 for vertical bar J(z)vertical bar less than or similar to 0.01. In contrast, the value of J(2)** increases quickly from J(2)* at vertical bar J(z)vertical bar less than or similar to 0.01 as the interplane coupling is further reduced. In addition, the magnetic correlation length is shown to directly depend on the nematic order parameter and thus exhibits a sharp increase (or jump) upon entering the nematic phase. Our results are broadly consistent with the predictions based on itinerant electron models of the iron-based superconductors in the normal state and, thus, help substantiate a classical spin framework for providing a phenomenological description of their magnetic properties.