For a diblock copolymer with total chain length γ > 0 and mass ratio m ∈ (−1, 1), we consider the problem of minimizing the doubly nonlocal free energy E ε (u) = H(u) + 1 ε 2s Ω W (u) dx + 1 2 Ω (−γ 2 ∆) − 1 2 (u − m) 2 dx in a domain Ω, where H(u) is a fractional H s-norm with s ∈ (0, 1 2), and W is a doublewell potential. This arises in the study of micro-phase separation phenomena for diblock copolymers with nonlocal diffusions. On the unit interval, we identify the Γ-limit as ε → 0 + , and also find explicit isolated local minimizers associated the lamellar morphology phase in the case m = 0, provided that the chain is sufficiently short or the nonlocal interaction is sufficiently strong (i.e. as s → 0 +). We stress that such extra condition is new for the nonlocal case and is not present in the classical model. The proof, while elementary, requires a careful analysis of the nonlocal integrals.