Two AsyncTasks running in parallel while requesting with HttpClient

I have two classes extending AsyncTask, in which they return a JSON from a server. I'm using the following code to run them simultaneously:

if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.HONEYCOMB)
    AsyncTaskExemplo1.executeOnExecutor(AsyncTask.THREAD_POOL_EXECUTOR, "");
else
    contact.execute("");

if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.HONEYCOMB)
    AsyncTaskExemplo2.executeOnExecutor(AsyncTask.THREAD_POOL_EXECUTOR, "");
else
    contact.execute("");

I use the following code to create my connection:

public static HttpClient httpclient = new DefaultHttpClient();
public JSONObject GET(String url, JSONObject jsonObject) {
    InputStream inputStream = null;
    String result = "";
    JSONObject jArray = null;
    try {
        HttpGet httpGet = new HttpGet(url);
        if (jsonObject != null) {
            String json = "";
            json = jsonObject.toString();
            StringEntity se = new StringEntity(json);
            ((HttpResponse) httpGet).setEntity(se);
        }
        httpGet.setHeader("Accept", "application/json");
        httpGet.setHeader("Content-type", "application/json");
        HttpResponse httpResponse = httpclient.execute(httpGet);
        inputStream = httpResponse.getEntity().getContent();
        if (inputStream != null) {
            result = convertInputStreamToString(inputStream);
        } else {
            result = "Did not work!";
        }
    } catch (Exception e) {
        Log.d("InputStream", e.getLocalizedMessage());
    }

    if (result != null) {
        try {
            jArray = new JSONObject(result);
        } catch (JSONException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
    }

    return jArray;
}

When I run AsyncTask one after the other, they return the JSONs correctly, however, if I execute them simultaneously, ONE of them does not wait for the server to return and continues execution returning null in the 'GET' function of my code. >

I've read that Android does not support two simultaneous HTTP requests with the standard Apache HttpClient library.

Please, if someone has already faced a similar situation and can help me, I am very grateful.