retrieve all the transaction between two addresses
I don't believe you can do this with just a single API call. I'd return all the transactions from one of the addresses, and cycle through all the inputs and outputs and if they match the other address then show the tx data.

Not sure which language you're using but the logic should be the same. 

&lt;?php
$addr1 = "1EipJdYVJbqsTSQhj1icK424AkMbyjvgBm";
$addr2 = "1LWwLvKWbcpiZYqCcwfuQ3gjjNJkxftmEJ";

$url = "https://blockchain.info/address/".$addr1."?format=json";
$fgc = json_decode(file_get_contents($url), true);

//num of txs
$txs = count($fgc["txs"]);

//loop through all txs
for($i=0;$i&lt;$txs;$i++){
    //check all inputs &amp; outputs for the other address
    //inputs
    $numinputs = count($fgc["txs"][$i]["inputs"]);
    for($ii=0;$ii&lt;$numinputs;$ii++){
        if($fgc["txs"][$i]["inputs"][$ii]["prev_out"]["addr"] == $addr2){
            //found a corresponding tx
            print_r($fgc["txs"][$i]);
        }
    }//end inputs loop

    $numoutputs = count($fgc["txs"][$i]["out"]);
    for($iii=0;$iii&lt;$numoutputs;$iii++){
        if($fgc["txs"][$i]["out"][$iii]["addr"] == $addr2){
            //found a corresponding tx
            print_r($fgc["txs"][$i]);
        }
    }//end outputs loop
}

?&gt;


http://phpfiddle.org/main/code/8imw-ardy