AFAIK Interpolations.jl should “just work”:
julia> data = [[1 2; 3 4], [5 6; 7 8]]
2-element Array{Array{Int64,2},1}:
[1 2; 3 4]
[5 6; 7 8]
julia> itp = interpolate(data, BSpline(Linear()))
2-element interpolate(::Array{Array{Int64,2},1}, BSpline(Linear())) with element type Array{Float64,2}:
[1 2; 3 4]
[5 6; 7 8]
julia> itp[1.0]
2×2 Array{Float64,2}:
1.0 2.0
3.0 4.0
julia> itp[1.1]
2×2 Array{Float64,2}:
1.4 2.4
3.4 4.4