Something like this would basically work:
preg_split('/(<strong>|<b>)/', $html1, 3, PREG_SPLIT_DELIM_CAPTURE | PREG_SPLIT_NO_EMPTY);
Given your test string of:
$html1 = '<strong>My content</strong>This is my content.<b>Some more bold</b>content';
you'd end up with
Array (
[0] => <strong>
[1] => My content</strong>This is my content.
[2] => <b>
[3] => Some more bold</b>content
)
Now, if your sample string did NOT start with strong/b:
$html2 = 'like the first, but <strong>My content</strong>This is my content.<b>Some more bold</b>content, has some initial none-tag content';
Array (
[0] => like the first, but
[1] => <strong>
[2] => My content</strong>This is my content.
[3] => <b>
[4] => Some more bold</b>content, has some initial none-tag content
)
and a simple test to see if element #0 is either a tag or text to determine where your "second tag and onwards" text starts (element #3 or element #4)