Why can we ignore the interaction between heat reservior and our system in canonical ensemble? When we derive the expression of canonical ensemble, we write the Hamiltonian of the whole system which contains our system and a heat reservior in the form,
$$
H_{\text{whole}} = H_1(\boldsymbol x) + H_2(\boldsymbol y)
$$
$\boldsymbol x, \boldsymbol y$ are coordinates of our system and the heat reservior respectively. But we assume they are in thermal equilibrium and can transfer heat to each other, which means they must have interaction, that is,
$$
H_{\text{whole}} = H_1(\boldsymbol x) + H_2(\boldsymbol y) + H_{\text{int}}(\boldsymbol x, \boldsymbol y)
$$ 
Why can we ignore the interaction term and continue the derivation.
 A: The magnitude of interaction energy of macroscopic systems is, in case of systems describable by the Boltzmann distribution, negligibly small compared to energy of the interaction systems. This is because the intermolecular forces decay fast with distance, so only those molecules near the interface contribute.
That is one justification for omitting the interaction term, but obviously it is valid only insofar magnitude of energy is the question. In other questions (correlation of systems), mere presence of the term may be important, irrespective of its magnitude.
The small value of interaction energy is true for macroscopic parcels of gas, but fails in case of gravitational systems, such as globular clusters or galaxies of stars, which is why Boltzmann's distribution is not completely correct for such systems (especially for high speeds, which are present in gas but much less so in gravitational systems - such particles escape the system so high speeds are less present).
A: The canonical ensemble is in thermal equilibrium with a heat bath at a fixed temperature.
A: The two systems are in thermodynamic equilibrium and exchange energy without losses. The reservoir is supposed to be so large that no matter how large the energy exchange, the temperature of the reservoir does not change.
The total energy of the system is thus simply the sum of the energy of the individual systems. By construction, there is no extra energy required for the energy exchange between the two systems. Therefore you don't need another term in the Hamiltonian to describe the interaction.
This whole construction has the goal of realising a system (the smaller one) with a well-defined temperature.
