  Line intensity mapping (LIM) experiments probing the nearby universe can
expect a considerable amount of cosmic infrared background (CIB) contiuum
emission coming from near and far-infrared galaxies. For the purpose of using
the LIM data to constrain the star formation rate (SFR), we argue that the CIB
continuum - traditionally treated as contamination - can be combined with the
LIM signal to enhance the SFR constraints achievable. We first present a power
spectrum model that is capable of joining continuum and line emissions that
assume the same prior SFR model. We subsequently analyze the effectiveness of
the joint model in the context of the EXperiment for Cryogenic Large-Aperture
Intensity Mapping (EXCLAIM), which utilizes the [CII] molecular line to study
the SFR. We numerically compute the theoretical power spectra according to our
model and the EXCLAIM survey specifics, and perform Fisher analysis to obtain
SFR parameter constraints. We find that although the joint model has no
considerable advantage over LIM alone assuming the current survey level of
EXCLAIM, its effects become significant when we consider more optimistic values
of survey resolution and angular span that are expected of future LIM
experiments. By manipulating the Fisher formalism, we show that the CIB is not
only an additional SFR sensitive signal, but also serves to break the SFR
parameter degeneracy that naturally emerges from the [CII] Fisher matrix. For
this reason, addition of the CIB will allow improvements in the survey
parameters to be better reflected in the SFR constraints, and can be
effectively utilized by future LIM experiments.
