Exotic hadrons are the very interesting research subjects in hadron and nuclear physics. The $X$, $Y$ and $Z$ tetraquarks, and the $P_c$ pentaquarks have a heavy quark and an anti-heavy quark. The heavy quark spin (HQS) doublet structure of the single heavy hadron like $D$ and $D^*$ meson is well known. On the other hand, the HQS multiplet structure of the doubly heavy hadron such as $Q\bar{Q}qqq$-type pentaquark has not been researched much. We study the HQS multiplet structure of the $Q\bar{Q}qqq$-type pentaquarks treated as the hadronic molecular state of a heavy meson and a heavy baryon. The light-cloud spin (LCS) basis is defined to study the HQS multiplet of the doubly heavy quark system. Introducing the LCS basis, there exist four- and ten-types of the HQS multiplet classified by the LCS structure for S- and P-wave $\bar{P}^{(*)}\Sigma_Q^{(*)}$ molecular states, respectively.