[Multisite]How can I update custom blog option?

As per the Codex on update_blog_option:

Switches to the blog id specified, runs update_option() and then
restores to the current blog. If $refresh is true then it will refresh
the blog details.

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Not tested, but I think your problem is trying to update elements of the array instead of the whole thing:

$the_options = get_blog_option($blog_id, 'mytheme_options');//retrieve all options

$the_options['country_base'] = $the_country;
$the_options['currency_unit'] = $d_currency;

update_blog_option($blog_id, 'mytheme_options', $the_options);