We construct a lattice model of compact (2+1)-dimensional Maxwell-Cher
n-Simons theory, starting from its formulation in terms of gauge invar
iant quantities proposed by Deser and Jackiw. We thereby identify the
topological excitations and their interactions. These consist of monop
ole-antimonopole pairs bounded by strings carrying both magnetic flux
and electric charge. The electric charge renders the Dirac strings obs
ervable and endows them with a finite energy per unit length, which re
sults in a linearly confining string tension. Additionally, the string
s interact via an imaginary, topological term measuring the (self-)lin
king number of closed strings.