The phase behavior of mixtures of flexible homopolymer chains with oligomers capable of hydrogen bonding with the monomer units of the polymer chains is analyzed in the weak segregation limit. A theoretical model is proposed to describe hydrogen bond (hb) formation depending on temperature, composition, and strength of hydrogen bonding. The conditions for macro-and microphase separation are studied. Microphase separation takes place if the tendency to segregate is not very strong and the degree of association X is large enough. The type of ordered structure depends not only on the composition and the temperature but also on the possibility to minimize the polymer-oligomer contacts. The period of the ordered structures D is minimal for stoichiometric composition of the mixture and increases with an increase of either component. Macrophase separation into ordered and homogeneous phases is typical for these kind of systems. The corresponding regions of phase coexistence occupy a significant part of the phase diagrams. Coexistence between different ordered phases such as lamellar and hexagonal can also take place. It was found that macrophase separation influences hb formation, reducing the average degree of association. The specific temperature dependence of the degree of association can result in the phenomenon of reappearing phases.