The origin of broadband emission is studied using temperature-dependent time-resolved photoluminescence (PL) spectra for two-dimensional (2D) layered halide perovskites (i.e., (PEA)2PbBr4 = phenylethylammonium lead bromide and (PEA)2PbI4 = phenylethylammonium lead iodide) semiconductors. Both perovskite systems show only a single peak exciton emission at room temperature, which becomes multipeak exciton emissions at low temperatures. For temperatures below 100 K, the (PEA)2PbBr4 film gives broad PL emission, Stokes shifted by 750 meV from narrow exciton emission peaks, whereas the (PEA)2PbI4 film does not show any broad emission. Kinetics of various peaks could provide useful insight to propose a consistent energy level scheme associated with a barrier (PEA) and well (PbX64-) material system's electronic states. This broad emission in (PEA)2PbBr4 perovskite is observed due to coupling of triplet states in the inorganic well (PbBr64-) and organic barrier (PEA) layer, which is in contrast to a proposed model based on self-trapped exciton.