Generalised Array Riffle

Python 2, 54

lambda B,*X:map(B.insert,*zip(*sorted(zip(*X))[::-1]))

Takes input as B,I,V. Modifies the input B when called (thanks to Martin Büttner for reminding me this is possible).

Uses map to call B.insert on each index/element pair. To avoid the issue of the list indices shifting as elements are inserted, sorts the pairs in decreasing order of index by an ugly zip/sort/unzip. If not for the shifting issue, we could just do map(B.insert,*X).

Old method (65):

B,V,I=input()
for i,v in sorted(zip(I,V))[::-1]:B[i:i]=v,
print B

Pyth, 14 bytes

s.icFPQmedSCtQ

Demonstration.

This program takes the inputs as a 3-tuple of lists in the order Base, Indices, Values.

Explanation on the example [5, 1, 4, 1, 3], [5, 0, 3], [0, 0, 7]:

1. Take the input: implicit, Q is the input.

2. Make the index, value pairs: CtQ = [(5, 0), (0, 0), (3, 7)]

3. Sort the pairs into increasing index order: SCtQ = [(0, 0), (3, 7), (5, 0)]

4. Take the value out of each pair: medSCtQ = [0, 7, 0]

5. Split the base list at the location of the indicies: cFPQ = [[], [5, 1, 4], [1, 3], []]

6. Interleave 3 and 4: .icFPQmedSCtQ = [[], 0, [5, 1, 4], 7, [1, 3], 0, []]

7. Combine into one list: s.icFPQmedSCtQ = [0, 5, 1, 4, 7, 1, 3, 0]

Haskell, 62 bytes

import Data.List
f b v i=map snd$sort$zip[0.5,1.5..]b++zip i v

Usage example: f [5,1,4,1,3] [0,0,7] [5,0,3] -> [0,5,1,4,7,1,3,0].

How it works: augment the base list with "and-a-half" indices starting at 0.5 (e.g. [(0.5,5),(1.5,1),(2.5,4),(3.5,1),(4.5,3)]) and concatenate it with the index-value pairs. Sort and discard the index.

Remark: don't know if I'm cheating here. From a mathematical point of view it's fine, but a programmer might argue that the list of indices [5,0,3] is not a list of Integers as requested, but a list of Fractionals (to be exact, the type is polymorphic, but must belong to the Fractional class, e.g. Float or Double).