This paper deals with a set membership approach to design an Unknown Input Interval Observer for uncertain Linear Time-Invariant (LTI) continuous-time systems. The goal is to compute lower and upper bounds for unmeasured state as well as unknown inputs. The bounds are guaranteed under the assumption that external disturbances and noises are bounded with a priori known bounds. The proposed interval observer structure is based on decoupling the unknown input effect on the state dynamics by solving algebraic constraints on the estimation errors. Numerical simulations on a 5th-order lateral axis model of a fixed-wing aircraft are provided to demonstrate the efficiency of the proposed technique.