  In this paper, we show that the pointwise finite-dimensional two-parameter
persistence module $\mathbb{HF}_*^{(\bullet,\bullet]}$, defined in terms of
interlevel filtered Floer homology, is rectangle-decomposable. This allows for
the definition of a barcode $\mathcal{B}_*^{(\bullet,\bullet]}$ consisting only
of rectangles in $\mathbb{R}^2$ associated with
$\mathbb{HF}_*^{(\bullet,\bullet]}$. We observe that this rectangle barcode
contains information about Usher's boundary depth and spectral invariants
developed by Oh, Schwarz, and Viterbo. Moreover, we establish relevant
stability results, particularly concerning the bottleneck distance and Hofer's
distance.
