If you want to use Armorys data youll need to call its methods to retrieve it.
There is no official API but Armory uses the same method names as their Blizzard
counterparts, e.g. Armory:UnitClass() will return the same information as 
Blizzards UnitClass() but then for the currently selected character.

Most likely you want to iterate through the stored inventory data. To accomplish 
this you need to save the current character, loop through the data and restore 
the saved character when youre done.
You can use profiles to save, select and restore the selected character.

Your basic layout will be:

    local currentProfile = Armory:CurrentProfile();
    for _, realm in ipairs(Armory:RealmList()) do
        for _, character in ipairs(Armory:CharacterList(realm)) do
            Armory:LoadProfile(realm, character);
            ...
        end
    end
    Armory:SelectProfile(currentProfile);

As an alternative you can also use:

    local currentProfile = Armory:CurrentProfile();
    for _, profile in ipairs(Armory:Profiles()) do
        Armory:SelectProfile(profile);
        ...
    end
    Armory:SelectProfile(currentProfile);

The SelectProfile() method uses an associative array that holds the realm and
character names (respectively profile.realm and profile.character).

The following example will count a specific item in the bags of your alts. It also
shows the use of some other methods that may be useful.

function Armory_GetItemCount(itemid)
    local currentProfile = Armory:CurrentProfile();
    local currentRealm = GetRealmName();
    local count = 0;
    local itemId, itemCount;

    if ( not (Armory and Armory:HasInventory()) ) then
        return 0;
    end

    for _, character in ipairs(Armory:CharacterList(currentRealm)) do
        Armory:LoadProfile(currentRealm, character);
        if ( not Armory:IsPlayerSelected() ) then
            for id = BACKPACK_CONTAINER, NUM_BAG_SLOTS do
                for index = 1, Armory:GetContainerNumSlots(id) do
                   itemId = (Armory:GetContainerItemLink(id, index) or ""):match("item:(%d+)");
                   if ( itemId == itemid ) then
                       _, itemCount = Armory:GetContainerItemInfo(id, index);
                       count = count + (itemCount or 0);
                   end
               end
            end
        end
    end

    Armory:SelectProfile(currentProfile);

    return count;
end

For instance Armory_GetItemCount("6948") will return the total number of hearthstones
possessed by your alts (useless information but you get the picture).