In the checkout, the recurring subtotal doesn't also include the disocunt from discount code. How can I resolve this?

This happens because Shopify Checkout shows the recurring price without any shipping, tax and applicable discounts. You can see this if you put your mouse cursor over the question mark next to the "Recurring subtotal" text (see screenshot). 
As we don't have control over that part of the system (only Shopify can control that), you could use a workaround to resolve this. A workaround for this would be to change the "Recurring total" text to something which will let customers know that this price doesn't include discounts. This way, they will know that even if they don't hover their mouse cursor over the question mark.
You can change this "Recurring subtotal" text in Shopify admin > Online store > click the three dots at the published theme > Edit default theme content.