In Information-Centric Networking (ICN), consumers send interest packets to the network and receive data packets as a response to their request without taking care of the producers, which have provided the content, contrary to conventional IP networks. ICN supports the use of multiple paths; however, with multiple consumers and producers, coordination among the nodes is required to efficiently use the network resources. Network coding (NC) is a promising tool to address this issue. The challenge in the case of NC is to be able to get independent coded content in response to multiple parallel interests by one or several consumers. In this work, we propose a novel construction called MILIC (Multiple Interests for Linearly Independent Contents) that impose constraints on how the replies to interests are coded, intending to get linearly independent contents in response to multiple interests. Several protocol variants, called MICN (MILIC-ICN), built on top of NDN (Named Data Networking), are proposed to integrate these interest constraints and NC of data packets. Numerical analysis and simulations illustrate that the MILIC construction performs well and that the MICN protocols are close to optimal throughput on some scenarios. MICN protocols compare favorably to existing protocols and show significant benefits when considering the total number of transmitted packets in the network, and in the case of high link loss rate.