  A barcode is a finite multiset of intervals on the real line.
Jaramillo-Rodriguez (2023) previously defined a map from the space of barcodes
with a fixed number of bars to a set of multipermutations, which presented new
combinatorial invariants on the space of barcodes. A partial order can be
defined on these multipermutations, resulting in a class of posets known as
combinatorial barcode lattices. In this paper, we provide a number of
equivalent definitions for the combinatorial barcode lattice, show that its
M\"obius function is a restriction of the M\"obius function of the symmetric
group under the weak Bruhat order, and show its ground set is the
Jordan-H\"older set of a labeled poset. Furthermore, we obtain formulas for the
number of join-irreducible elements, the rank-generating function, and the
number of maximal chains of combinatorial barcode lattices. Lastly, we make
connections between intervals in the combinatorial barcode lattice and certain
classes of matchings.
