It's not entirely clear what you want to achieve.
If you want to /match this here/ and then print the next line then
sed -n '/match this here/{n;p}' /my/log/file.log
DETAIL: parameters: also want to filter this line
If you want to /match this here/ and then print the matched line and the one following it then
sed -n '/: match this here/{p;n;p}' /my/log/file.log
LOG: execute <unnamed>: match this here
DETAIL: parameters: also want to filter this line
With grep you can
grep -A 1 'match this here' /my/log/file.log
LOG: execute <unnamed>: match this here
DETAIL: parameters: also want to filter this line
if you have multiple matches each is separated by --
grep -A 1 'match this here' /my/log/file.log
LOG: execute <unnamed>: match this here
DETAIL: parameters: also want to filter this line
--
LOG: execute <unnamed>: match this here
DETAIL: parameters: also want to filter this line
And you can
grep -A 1 'match this here' /my/log/file.log | grep -v 'match this here'
to remove the first line if that's what you want.