Draw some ASCII-boxes

Python 2, 117 Bytes

def f(h,v):r="+"+"+".join("-"*i for i in h)+"+\n";print r+r.join(("|"+"|".join(" "*i for i in h)+"|\n")*i for i in v)+r

Try it on ideone.

Not expecting too much from this. Really simple, just uses python joins and string multiplication to pull everything together.

JavaScript (ES6), 83 bytes

(a,b,g=(a,[s,t])=>t+a.map(n=>s.repeat(n)+t).join``+`
`)=>g(b,[g(a,` |`),g(a,`-+`)])

Output includes two trailing newlines.

MATL, 25 22 21 bytes

'|-+ '2:"1tiYsQ(]E!+)

Uses inputs with 1 added (allowed by the challenge).

Try it online!

Explanation

The code initially builds an array containing 1 for the column indices of non-space characters in the final result, and 0 otherwise. So if the first input is [2 1 4 1 3 1] (would be [1 0 3 0 2 0] in the 0-based format) this array will be

1 0 1 1 0 0 0 1 1 0 0 1 1

Note how the length of runs of zeros is related to the input. Specifically, this array is built as follows:

1. Initiallize the array to a single 1.
2. Compute the cumulative sum of the input and add 1. In the example this gives [3 4 8 9 12 13].
3. Extend the array from step 1 by assigning 1 to the entries with (1-based) indices given by step 2. Intermediate entries are automatically set to 0.

A similar array is built for the rows. Second input [3 2 1 1] (or [2 1 0 0 ]) gives

1 0 0 1 0 1 1 1

Now the second array is multiplied by 2, transposed and added with broadcast to the first. This gives the 2D array

3 2 3 3 2 2 2 3 3 2 2 3 3
1 0 1 1 0 0 0 1 1 0 0 1 1
1 0 1 1 0 0 0 1 1 0 0 1 1
3 2 3 3 2 2 2 3 3 2 2 3 3
1 0 1 1 0 0 0 1 1 0 0 1 1
3 2 3 3 2 2 2 3 3 2 2 3 3
3 2 3 3 2 2 2 3 3 2 2 3 3
3 2 3 3 2 2 2 3 3 2 2 3 3

Indexing into the string '|-+ ' gives the final result as a 2D char array. Since indexing is modular and 1-based, index 0 corresponds to the last element (space).

'|-+ '                   % Push this string
      2:"       ]        % Do this twice
         1               % Push 1 (initial array)
          t              % Push another 1 (contents to be filled in)
           i             % Take input
            Ys           % Cumulative sum
              Q          % Add 1
               (         % Fill 1 into those entries of the array
                 E       % Multiply by 2
                  !      % Transpose
                   +     % Add, with broadcast
                    )    % Index (modular, 1-based) into the string