To maintain C1 continuity between consecutive (cubic) Bézier splines you have to maintain the following equations:
P3(i-1) - P2(-1) = P1(i) - P0(i)
P3(i-1) = P0(i)
where the index in the parenthesis represents the index of the curve in the spline. The derivative/tangent at the beginning (end) of Bézier curve is in fact parallel to the edge between the first two (last two) control points. If the two curves have different degree you have to multiply each part of the equation with the degree of the corresponding curve.