DATATYPE H5T_COMPOUND {
    H5T_IEEE_F32LE "X";
    H5T_IEEE_F32LE "Y";
}

With[
 {
  file = FileNameJoin[{Directory[], subfolderWithExamples, "h5ex_t_cmpd.h5"}],
  dataSet = "DS1"
  },
 CompoundDataType`Information[file, dataSet]
 ]
(*
{"DataSpaceDimensions" -> {4},
 "MemberDataTypeClass" -> {0, -3, 1, 1},
 "MemberMemorySize" -> {8, 8, 8, 8},
 "MemberName" -> {"Serial number"  , "Location",
                  "Temperature (F)", "Pressure (inHg)"},
 "MemberOffset" -> {0, 8, 20, 28},
 "MemberSize" -> {8, 8, 8, 8},
 "MemoryDataTypeSize" -> 32,
 "NumberOfMembers" -> 4}
*)

Needs["h5dumpImport`"]
datasets = Import["testData.h5", {"Datasets"}];
dumpFile = h5dump["/usr/bin/h5dump", "testData.h5", datasets[[1]]];
dumpImport = h5dumpImportNew[h5dumpImport[], dumpFile];
dumpImport.h5dumpImportData[All]
dumpImport.h5dumpImportClose[];

{{1, 11, 111, 1111, 11111, 111111, 1111111, 1.1, 11.11, "one"},
 {2, 22, 222, 2222, 22222, 222222, 2222222, 2.2, 22.22, "two"},
 {3, 33, 333, 3333, 33333, 333333, 3333333, 3.3, 33.33, "three"}}

In[3]:= Import["ExampleData/sample2.h5", "/Compound"]

Out[3]= {
  {
    <|
      "Country" -> "Botswana",
      "Military" -> {5.3, 4.5},
      "Elevation" -> <|"Max" -> 4892, "Min" -> 513, "Highest point" -> "Otse Hill"|>
    |>,
    <|
      "Country" -> "Chile",
      "Military" -> {8.8, 3.7},
      "Elevation" -> <|"Max" -> 6893, "Min" -> 0, "Highest point" -> "Ojos del Salado"|>
    |>
  }, {
    <|
      "Country" -> "France",
      "Military" -> {5.3, 3.3},
      "Elevation" -> <|"Max" -> 4810, "Min" -> -10, "Highest point" -> "Mont Blanc"|>
    |>,
    <|
      "Country" -> "Laos",
      "Military" -> {18.9, 4.3},
      "Elevation" -> <|"Max" -> 2817, "Min" -> 70, "Highest point" -> "Phou Bia"
    |>
  |>
}}

In[2]:= Import["ExampleData/sample2.h5", {"DataFormat", "/Compound"}]

Out[2]= <|
  "Class" -> "Compound",
  "Structure" -> <|
    "Country" -> "String",
    "Military" -> <|"Class" -> "Array", "Dimensions" -> {2}, "DataFormat" -> "Real64"|>,
    "Elevation" -> <|
      "Class" -> "Compound",
      "Structure" -> <|"Max" -> "Integer16", "Min" -> "Integer16", "Highest point" -> "String"|>
    |>
  |>
|>